Anomalous Thermalization in Quantum Collective Models

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Information theory

Background:

• Thermalized states are typically assumed to lose memory of their preparation.
• Nonequilibrium processes can probe subtle properties of quantum systems.
• Quantum fluctuation theorems describe statistical properties of work in quantum processes.

Purpose of the Study:

• To investigate if apparently thermalized quantum states store information about their past.
• To develop and test a condition for the microcanonical quantum Crook's theorem.
• To determine if testing quantum fluctuation theorems is essential for verifying thermalization.

Main Methods:

• Numerical experiments using the Lipkin-Meshkov-Glick and Dicke models.
• Analysis of work statistics in nonequilibrium processes.
• Comparison of microcanonical averages with quantum fluctuation theorems.

Main Results:

• Apparently thermalized states were shown to store information about their past.
• The microcanonical quantum Crook's theorem was found to fail in specific scenarios within the tested models.
• Different preparation procedures or trajectories led to different work statistics, even for the same equilibrium states or protocols.

Conclusions:

• Testing quantum fluctuation theorems is mandatory to rigorously verify if a quantum system is properly thermalized.
• The study demonstrates that information about the system's history can persist even in equilibrium states.
• The findings challenge the assumption that thermalization erases all memory of the system's past.